What are the major differences between cost, loss, error, fitness, utility, objective, criterion functions?
What are the major differences between cost, loss, error, fitness, utility, objective, criterion functions?

We can first consider what kind of elements are in this list.  They are all quantifications that guide a process of adaptation, learning, or innovation — controls a process that optimizes or attempts to optimize the development of another process.  Quantification allows for comparison and the determination of first and second-degree derivatives to use in approximating steps in improvement.
On the basis of this generalization, the list may be expanded to include other potential quantifications that can control.

Pain
Pleasure
Disparity
Value
Advantage
Expense
Profit
Gain
Return
Distance
Burden
Optimality

In English, there is quite a bit of nuance in terms of normal contextual use.  In academic papers on machine learning topics there are some conventions forming there, producing jargon, meanings beyond the normal English use.  We can first divide them symmetrically around the most basic qualifier.  Is the increase in the number what is intended or something to be avoided?
Decreases are Desirable

Cost
Loss
Error
Distance
Pain
Disparity
Expense
Burden

Increases are Desirable

Fitness
Utility
Objective
Criterion
Pleasure
Value
Advantage
Profit
Gain
Optimality
Complete

Other Features
Some of these are relative, such as Advantage being a relative measure between two Values associated with two Action options.  Some are direct inversions, as in that the quotient of Gain over Loss equals -1 in the usual contexts of those words.  Some appear to be opposite but in fact are not, as in the case of pain and pleasure occurring concurrently and via different neural mechanisms in biological neural systems.
Some are discrete and have only two possible values, such as Criterion and Complete.  Those can be well represented by Boolean values rather than integers, fixed-point, or floating-point numbers.
Some are conditionally synonymous, as in the case of Distance and Error if the output dimensionality is one or the output is multidimensional but the error aggregation method used is the square root of the sum of squares.
Some seem better in financial contexts ... others in robotic contexts.
Words like Disparity and Optimality are generalizations.
One, in particular, is a quotients based on investment &amp;mdash Return — which could be applied to energy return on energy invested (as Hall suggests is the fitness function for genetic evolution).
What is missing from this list is learning based on multiple degrees of freedom, not used in mainstream ML yet, and probably will emerge in papers and then libraries and then VLSI designs in time.  This likely direction would introduce the plurals of many of these quantifications because it will be vectors of corrective signaling back-propagating to perform curved modifications on network parameters.  It is likely that brain signaling (pulses, energy balances, neurochemical secretions and uptake, and genetic expression) will not be well simulated until this happens.
In all cases, it is the definition of these quantifications that drive adaptation, learning, and innovation in biological and artificial systems.  It is thus likely that the application of ethics and risk analysis might best be applied to AI in the formulation of the calculation of these quantities in adaptive systems.